The Seaworld parks' food and beverage policy is found here:
http://seaworldparks.com/en/seaworld-orlando/park-info/food-and-beverage-policy/
Basically, unless you have special dietary concerns which necessitate you bringing your own food, you should plan on purchasing your meals and snacks inside the park.
Now...that said....dining at SW (and the sister parks) is MUCH cheaper than dining at Disney. And the SW parks each offer an all-day dining option which is open to every guest, not just those staying onsite like Disney. Another bonus is that's it truly unlimited from breakfast right through to 30 minutes prior to park closing, and it includes unlimited drinks and snacks as well (from participating restaurants, not from the snack carts). There are lots of healthy options, too, from fettucini alfredo to barbecued chicken, from fruit cups to salads and wraps, so just don't think hot dogs and french fries.
That means a cold bottle of water whenever you need it. On a hot day, we can drink our plan value alone!
SW's all-day dining price varies by season. Its usually between $29.99 and $34.99 per adult. We snagged it for $24 pp on the annual "Blue Friday" sale (held on the Black Friday weekend each year). Considering that includes breakfast, lunch, dinner, all the drinks we want, and unlimited in-between food, you can't beat it!!
http://seaworldparks.com/en/seaworld-orlando/dine-and-shop/dining/all-day-dining-deal/
Aquatica's all day dining is $18 pp. Its a little different than the SW plan, as its at one restaurant only (the Banana Beach Buffet). But again, you can visit as many times as you wish throughout the day for the one price. And again, we picked up dining passes on Blue Friday for $12 (a $6 saving pp)...making it an incredible value. Where else can you eat all day long (breakfast excluded, as the Banana Beach Buffet doesn't open until 11 IIRC) for $12? That's as cheap as one adult meal at Typhoon Lagoon or Blizzard Beach (and the food is comparable in quality).
http://aquaticabyseaworld.com/en/orlando/dine-and-shop/dining/banana-beach/
I haven't been to BG, but their all day dining plan is currently $32.99, and I believe it works the same as SW's plan:
http://seaworldparks.com/en/buschga...hop/dining/busch-gardens-all-day-dining-deal/
If you were looking for something different, SW offers "Dine with Shamu", a very diverse and flavorful buffet of sustainable foods (though still having many options that appeal to the young and young-at-heart) for $29.99 pp. Seating is right along the glass of the whale pool (on the opposite side of the One Ocean theater) and you get an up-close presentation by the killer whales and trainers that's really very cool. Much more affordable than the Disney buffets and it also includes a free 6 x 8 family photo.
If you still wish to eat a picnic lunch, I do believe there are picnic areas for guest use but they are located outside the park gates. So you would have to leave your food in your car, exit the park at meal time, eat your picnic lunch in the designated area, then re-enter the park afterward.
Since you have time to wait, I would definitely suggest holding off and watching for the meal plans on the Blue Friday sale. I think, particularly at SW, you would be very pleased with the options available. Its not your typical quick service (though those choices are available too). There are tons of non-burger, non-pizza selections available and their chocolate cake is heaven

.